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2016年3月5日 · The variables are uncorrelated but dependent. Alternatively, consider a discrete bivariate distribution consisting of probability at 3 points (-1,1),(0,-1),(1,1) with probability 1/4, 1/2, 1/4 respectively. Then variables are uncorrelated but dependent. Consider bivariate data uniform in a diamond (a square rotated 45 degrees).

2015年9月7日 · Here is the relationship: If X and Y are uncorrelated, then X-E[X] is orthogonal to Y-E[Y]. Unlike that independent is a stronger concept of uncorrelated, i.e., independent will lead to uncorrelated, (non-)orthogonal and (un)correlated can happen at the same time.

2015年10月10日 · $\begingroup$ here is an example from my textbook (p19, 5th ed, Montgomery, Peck Vining): in the derivation of Var[b], Var distributes across the summation "because the observations y are uncorrelated". Earlier in the book (p13): "the responses are uncorrelated" because "the errors are uncorrelated". $\endgroup$ –

2018年11月10日 · However, two variables that are uncorrelated AND jointly normally distributed are guaranteed to be independent. Can someone explain intuitively why this is true? What exactly does joint normality of two variables add to the knowledge of zero correlation between two variables, which leads us to conclude that these two variables MUST be independent?

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A time-honored reminder in statistics is "uncorrelatedness does not imply independence". Usually this reminder is supplemented with the psychologically soothing (and scientifically correct)

2022年2月17日 · Should two continuous variables be correlated to include their interaction? I.e. does y = x1 + x2 + x1x2 make sense if correlation between x1 and x2 is weak at -0.1, and their coefficients in the

2020年5月3日 · Terminologically, "uncorrelated" to me means that 2 things have no relationship, not necessarily constrained to linear relationships. However, in statistics, we seem to confine "uncorrelated" to mean 2 things have no linear relationship, but …

Two multiple regression coefficient estimates $\hat\beta_i$ and $\hat\beta_j$ are uncorrelated whenever either (or both) of the corresponding columns of the design matrix are orthogonal to all other columns. Many standard experimental designs consist of choosing values of the independent variables to make the columns mutually orthogonal.